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Option 6 (none of the above) being true would mean options 1-5 are false, but since then options 1-4 are false, option 5 (none of the above) would be true, forming a contradiction. Therefore, Option 6 is false.

Since option 6 is false, option 1 (all of the below) is false, meaning option 3 (all of the above) is false.

That leaves options 2, 4, and 5. If option 2 is true (none of the below), that would imply that 4 (one of the above) is false (by 2) and 4 is true (since only 2 above 4 is true), a contradiction. Therefore, 2 is false. Since 1, 2, and 3 are all false, 4 (one of the above) must therefore be false.

What’s left is 5 (none of the above). Since 1, 2, 3, and 4 are known to be false, that means 5 is true. 6 is also known to be false.

Option 5, because most multiple choice tests use two similar answers, where one is a “distractor”. The two most similar answer options are 5 and 6, but as stated above, 6 contradicts itself. No need to even consider options 1-4 in that context (though blaisepascal’s reasoning is sound)

We assume that there is a unique true option. It cannot be option 4, because then one of options 1, 2, and 3 would be true, contradicting uniqueness. So 4 is false; so 1, 2, and 3 are all false; so 5 is true.

Similar language (“fill in the bubble corresponding to the correct answer”) is in the instructions to the SAT, and it also includes “all of the above” answers. I doubt I’d ever have met Chad if he took the definite article that literally.

@Sridhar, @John Armstrong: The question cannot be “Which of the following is false?”:

1. Only one is false and all the others are true. (Given.)
2. Either 5 or 6 is true. (From 1.)
3. All “of the above” (1-4) are false. (From 2.)
4. 1 contradicts 3: 1-4 are false, but only one can be false.

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